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Recent problems solved by 'stanbon'
stanbon answered: 57339 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299 , 57300..57329 , 57330..57359, >>NextExponents/543362: Are any of these wrong? I've done the work, I would just like to know which ones are wrong please and thank you.
1. Simplify the following expression, and rewrite it in an equivalent form with positive exponents.
Answer: x^7 over y^5
2. Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression.
(-5x3y)2
Answer: 25x6y2
3. Short Answer: Simplify the following expression, and rewrite it in an equivalent form with positive exponents.(4x-2)-2
Solving: 4x*-2= -8x and -2*-2=4
Answer: -8x+4
4. Multiply the expressions, and simplify.
(x-2y3) • (2x4y-2)
Answer:2x-6y5
5. Short Answer: Convert this number to scientific notation:
64,000,000
Solving: 64,000,000 divided by 10^7= 6.4
Answer: 6.4*10^7
6. Use scientific notation to divide the following two numbers. Express the answer using scientific notation; retain at least three decimal places.
(8.7 • 109) / (3.22 • 102)
Solving:(8.7/3.22)*10^7
Answer: 2.701* 10^7
7. Add the complex expressions, and simplify.
(-10 + 3.1i) + (-6.2 + 2.5i)
-16.2 + 5.6i
-10.6i
-21.8
-10.6
8. Short Answer: Simplify the following expression; express in terms of i.√ -36
Solving: i√-36= i(6)=6i
Answer: 6i
9. Simplify the following expression.√ -90√ -15
Solving: -15* -15* -15* -15* -15* -15=90
Answer: -15√6
1 solutions
Answer 354818 by stanbon(57412)   on 2011-12-07 14:14:41 (Show Source):
You can put this solution on YOUR website!1. Simplify the following expression, and rewrite it in an equivalent form with positive exponents.
Answer: x^7 over y^5 = y^2
-----------------------------
2. Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression.
(-5x3y)2
Answer: 25x6y2
Correct
----------------------------
3. Short Answer: Simplify the following expression, and rewrite it in an equivalent form with positive exponents.(4x-2)-2
Solving: 4x*-2= -8x and -2*-2=4
Answer: -8x+4
---
Are you sure the -2 is not an exponent?
Maybe your problem is (4x-2)^(-2) = 1/(4x-2)^2 = 1/(16x^2+16x+4)
----
4. Multiply the expressions, and simplify.
(x-2y3) • (2x4y-2)
Answer:2x-6y5
---
If those "-2's" are not exponents you should be using FOIL.
If they are exponents you have the wrong answer.
---------------------
5. Short Answer: Convert this number to scientific notation:
64,000,000
Solving: 64,000,000 divided by 10^7= 6.4
Answer: 6.4*10^7
Correct
---------------------
6. Use scientific notation to divide the following two numbers. Express the answer using scientific notation; retain at least three decimal places.
(8.7 • 10^9) / (3.22 • 10^2)
Solving:(8.7/3.22)*10^7
Answer: 2.702* 10^7
---
Correct
---------------------
7. Add the complex expressions, and simplify.
(-10 + 3.1i) + (-6.2 + 2.5i)
Answer: -16.2 + 5.6i
Correct
---------------------
8. Short Answer: Simplify the following expression; express in terms of i.√ -36
Solving: i√-36= i(6)=6i
Answer: 6i
----
No: (i)(sqrt(-36)) = i*6i = -6
----------------------------------
9. Simplify the following expression.√ -90√ -15
Solving: -15* -15* -15* -15* -15* -15=90
Answer: -15√6
-----
I don't understand your "solving" but the answer is correct.
===============================================================
Cheers,
Stan H.
|
Quadratic_Equations/543368: (2x-5)^2+4(2x-5)+3=0
1 solutions
Answer 354810 by stanbon(57412) on 2011-12-07 13:43:16 (Show Source):
You can put this solution on YOUR website!(2x-5)^2+4(2x-5)+3=0
-------
Let 2x-5 = w
===================
w^2+4w+3 = 0
Factor:
(w+3)(w+1) = 0
w = -3 or w = -1
--------------------
Solve for "x":
2x-5 = -3
2x = 2
x = 1
------
OR
---
2x-5 = -1
2x = 4
x = 2
-------
Final Solution: x = 1 or x = 2
================================
Cheers,
Stan H.
==============
|
Exponents/543255: The instructions say to simplify the following expression and rewrite it in an equivalent form with positive exponents.
24 x^10 y
__________
24 x^3 y^6
I am coming up with x^13y^7. Is this correct and if not can you please show me how to work this? Thanks!
1 solutions
Answer 354791 by stanbon(57412) on 2011-12-07 09:06:29 (Show Source):
You can put this solution on YOUR website!simplify the following expression and rewrite it in an equivalent form with positive exponents.
(24 x^10 y) / (24 x^3 y^6)
=================
= x^7/y^5
==============
Cheers,
Stan H.
|
Probability-and-statistics/543085: In some dice games, rolling two dice and getting two 6’s is called getting “boxcars.” What is the probability of rolling “boxcars” twice in a row?
1 solutions
Answer 354747 by stanbon(57412) on 2011-12-06 22:36:54 (Show Source):
You can put this solution on YOUR website!In some dice games, rolling two dice and getting two 6’s is called getting “boxcars.” What is the probability of rolling “boxcars” twice in a row?
-----
boxcars once: (1/36)
---
boxcars twice: (1/36)^2 = 1/1296
=========================================
Cheers,
Stan H.
====================
|
Numbers_Word_Problems/543101: The sum of two consecutive integers is 86. Find them using a variable.
1 solutions
Answer 354746 by stanbon(57412) on 2011-12-06 22:32:37 (Show Source):
You can put this solution on YOUR website!The sum of two consecutive integers is 86. Find them using a variable.
----
1st: x
2nd: x+1
---
Equation:
su = 86
2x+1 = 86
2x = 85
x = 42.5
Comment:
That is not an integer.
There are no consecutive integers whose sum = 86.
==========================
Cheers,
Stan H.
|
Probability-and-statistics/542974: A new automobile comes with the choices of 5 colors & 3 different engine types. Then there is a list of 12 possible options to include in your new car. you can choose any number of these options, from none to all 12. How many different possible automobiles must the factory be prepared to build.
I tried doing 5*3*12 but i wasnt sure if that was the correct way to solve the problem.. & then i attempted to use what is called nPr where i did 12! divided by 5!*3! but once again i wasnt quite sure if that was correct.. Help please?
1 solutions
Answer 354719 by stanbon(57412) on 2011-12-06 20:09:32 (Show Source):
You can put this solution on YOUR website!A new automobile comes with the choices of 5 colors & 3 different engine types. Then there is a list of 12 possible options to include in your new car. you can choose any number of these options, from none to all 12. How many different possible automobiles must the factory be prepared to build.
----
Each of the options is either chosen or not chosen: there are 2^12 possibilities.
======================
Ans: 5*3*2^12 = 61,440 different configurations
=====
Cheers,
Stan H.
=========
|
Travel_Word_Problems/542971: My teacher went over these problems in class today. I know that I would set up a chart to help me solve the problem, but I get stuck on how to determine the t in D=rt. Please help me!!! Thanks!!!
Two trains leave a station at the same time, heading in opposite directions. One train is traveling at 80 km/h, the other at 90 km/h. How long will it take for the trains to be 425 km apart?
1 solutions
Answer 354715 by stanbon(57412) on 2011-12-06 20:06:21 (Show Source):
You can put this solution on YOUR website!Two trains leave a station at the same time, heading in opposite directions. One train is traveling at 80 km/h, the other at 90 km/h. How long will it take for the trains to be 425 km apart?
----
1st train DATA:
rate = 80 km/hr ; time = t hrs ; distance = 80t km
---------------
2nd train DATA:
rate = 90 km/hr ; time = t hrs ; distance = 90t km
----
Equation:
distance + distance = 425 km
80t + 90t = 425
170t = 425
t = 2.5 hours
=================
Cheers,
Stan H.
=================
|
logarithm/542957: I need to Solve the equation log3 x^2 - log3(3x+18)=0
log is base 3 tried log3(x^2/3x+18)=0, not sure if this is right or how to proceed,
also tried to remove log3 ended with x^2-3x+18=0 removed 18from both sides x^2-3x=-18
tried to separate into to equations x=6, x=-3 neither fit into equation can not find another example in the book or in notes please help me figure out how to solve three of us and we still have no idea
1 solutions
Answer 354710 by stanbon(57412) on 2011-12-06 20:02:50 (Show Source):
You can put this solution on YOUR website!Solve the equation
log3 x^2 - log3(3x+18)=0
------------
log3[x^2/(3x+18)] = 0
x^2/(3x+18) = 3^0 = 1
----
x^2 = 3x+18
x^2-3x-18 = 0
---
Factor:
(x-6)(x+3) = 0
x = 6 or x = -3
====================
Cheers,
Stan H.
|
Probability-and-statistics/542707: A sample of 25 concession stand purchases at the October 22 matinee of Bride of Chucky showed a mean purchase of $5.29 with a standard deviation of $3.02. For the October 26 evening showing of the same movie, for a sample of 25 purchases the mean was $5.12 with a standard deviation of $1.98. The means appear to be very close, but not the variances. At α = .03, is there a difference in variances?
1 solutions
Answer 354697 by stanbon(57412) on 2011-12-06 19:14:50 (Show Source):
You can put this solution on YOUR website!A sample of 25 concession stand purchases at the October 22 matinee of Bride of Chucky showed a mean purchase of $5.29 with a standard deviation of $3.02. For the October 26 evening showing of the same movie, for a sample of 25 purchases the mean was $5.12 with a standard deviation of $2.14. The means appear to be very close, but not the variances. At the .05 level of significance, is there a difference in variances? Show all steps clearly, including an illustration of the decision rule.
---------------------------
Ho: s^2(matinee)=s^2(evening)
Ha: s^2(matinee) is not equal to s^2(evening)
-------------------------------
Two-tailed test with alpha = 0.05
------------------------------
Test Statistic: F = (2.14)^2/(3.02)^2 = 0.502127
-------------------------------
Critical Value:
numerator df's = 24 ; denominator df's = 24
F = 2.27
-----------
Conclusion:
Since the Test Statistic is less than the Critical Value, Fail to
reject Ho.
The variances for matinee and evening are statistically equivalent.
==============
Cheers,
Stan H.
|
Probability-and-statistics/542892: 22 out of 58 channels had commercials on
Find the probability of getting a value of the statistic that is smaller than or equal to 22.
(pˆ1 solutions
Answer 354696 by stanbon(57412) on 2011-12-06 19:10:58 (Show Source):
You can put this solution on YOUR website!22 out of 58 channels had commercials on
Find the probability of getting a value of the statistic that is smaller than or equal to 22.
----
sample proportion = 22/58 = 0.38
----
margin of error: sqrt[0.38*0.62/58] = 0.064
-----
Statistic <= 22 ??
That doesn't make any sense.
================================
Cheers,
Stan H.
|
Probability-and-statistics/542709: In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean crash damages the same for these three vehicles? Perform an ANOVA at α = 0.1.
Goliath Varmint Weasel
$1,600 $1,290 $1,090
$760 $1,400 $2,100
$880 $1,390 $1,830
$1,950 $1,850 $1,250
$1,220 $950 $1,920
1 solutions
Answer 354692 by stanbon(57412) on 2011-12-06 18:52:07 (Show Source):
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Probability-and-statistics/542738: •What is the probability that you and a friend both solve the same five problems?
The test has 6 questions, you are required to answer 3 given questions but can pick the other two questions from a pool of 3 questions.
1 solutions
Answer 354691 by stanbon(57412) on 2011-12-06 18:48:41 (Show Source):
You can put this solution on YOUR website!What is the probability that you and a friend both solve the same five problems?
The test has 6 questions, you are required to answer 3 given questions but can pick the other two questions from a pool of 3 questions.
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There are 3C2 = 3 sets of 2 questions
One of them is the same as your friends choice of 2.
P(choose same set of 2) = 1/3
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Cheers,
Stan H.
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Probability-and-statistics/542760: In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean crash damages the same for these three vehicles? Perform an ANOVA at α = 0.1.
Goliath Varmint Weasel
$1,600 $1,290 $1,090
$760 $1,400 $2,100
$880 $1,390 $1,830
$1,950 $1,850 $1,250
$1,220 $950 $1,920
Step 1: State the null and alternate hypotheses
Ho: u1 = u2 = u3
H1: At least one of the means id fifferent
Step 2: Select a level of significance
α = 0.1 The level of significance is 10%.
Step 3: Identify the test statistic
Step 4: Formulate a decision rule
Step 5: Make a decision
1 solutions
Answer 354690 by stanbon(57412) on 2011-12-06 18:45:21 (Show Source):
You can put this solution on YOUR website!In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated.Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean crash damages the same for these three vehicles? Crash1
Crash Damage ($)
Goliath Varmint Weasel
1,600 1,290 1,090
760 1,400 2,100
880 1,390 1,830
1,950 1,850 1,250
1,220 950 1,920
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Ho: means are all the same
Ha: at least one of the means is different
Chi-Sq Test:
Test Statistic: Chi-Sq = 1338.97
p-value: 0
df= 8
Conclusion: Reject Ho
At least one of the means is different
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Cheers,
Stan H.
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Probability-and-statistics/542850: Find the mean and standard deviation for 20 trials for a binomial probability distribution with a 40% chance of success on each trial?
1 solutions
Answer 354688 by stanbon(57412) on 2011-12-06 18:34:48 (Show Source):
You can put this solution on YOUR website!Find the mean and standard deviation for 20 trials for a binomial probability distribution with a 40% chance of success on each trial?
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mean = np = 20*0.4 = 8
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std = sqrt(npq) = sqrt(8*0.6) = 2.19
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Cheers,
Stan H.
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Probability-and-statistics/542853: A new headache remedy has been found to begin causing relief from headaches with a normal distribution with a mean of 25 minutes and standard deviation of 8 minutes.
If a headache sufferer takes this medication, what is the probability that she will feel relief in 30 minutes or less?
1 solutions
Answer 354684 by stanbon(57412) on 2011-12-06 18:27:44 (Show Source):
You can put this solution on YOUR website!A new headache remedy has been found to begin causing relief from headaches with a normal distribution with a mean of 25 minutes and standard deviation of 8 minutes.
If a headache sufferer takes this medication, what is the probability that she will feel relief in 30 minutes or less?
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z(30) = (30-25)/8 = 5/8
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P(x <= 30) = P(z <= 5/8) = 0.2660
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Cheers,
Stan H.
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Linear-equations/542848: Can you help me with this homework question ...
Kate is SCUBA diving on the Bahamas. She is currently 135 feet under water but she is swimming towards the surface at a rate of 15 feet per minute. Write an equation that represents the time, in minutes, and y represents Kate's depth underwater
1 solutions
Answer 354679 by stanbon(57412) on 2011-12-06 18:20:17 (Show Source):
You can put this solution on YOUR website!Kate is SCUBA diving on the Bahamas. She is currently 135 feet under water but she is swimming towards the surface at a rate of 15 feet per minute. Write an equation that represents the time, in minutes, and y represents Kate's depth underwater.
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y = 15x - 135
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Cheers,
Stan H.
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Linear-equations/542844: write an equation that is parallel to the graph of the line that passes though the points (-8,2) and (-3,3)?
1 solutions
Answer 354676 by stanbon(57412) on 2011-12-06 18:14:41 (Show Source):
You can put this solution on YOUR website!write an equation that is parallel to the graph of the line that passes though the points (-8,2) and (-3,3)?
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slope = (3-2)/(-3--8) = 1/5
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Equation:
y = (1/5)x
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Cheers,
Stan H.
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Probability-and-statistics/542690: A manufacturing process produces bags of cookies. The distribution of content weights of these bags is Normal with mean 15.0 oz and standard deviation 1.0 oz. We will randomly select n bags of cookies and weigh the contents of each bag selected.
Which of the following statements is true with respect to the sampling distribution of the sample mean?
1 solutions
Answer 354656 by stanbon(57412) on 2011-12-06 16:07:15 (Show Source):
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Graphs/542680: Determine the domain and range (image) of:
F(x) = ((-7) / (2 x - 5))
I want the answer and to get it too. Please
Thank you
1 solutions
Answer 354650 by stanbon(57412) on 2011-12-06 15:51:37 (Show Source):
You can put this solution on YOUR website!domain and range (image) of:
F(x) = ((-7) / (2 x - 5))
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Domain ?:
The denominator cannot be zero.
2x-5 = 0
x = 5/2
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Domain is "All Real Numbers except x = 5/2."
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Range ?
y = (0x/2x) = 0/2 = 0
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Range is "All Real Numbers except y = 0".
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Cheers,
Stan H.
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test/542668: Solve i^-4003
1 solutions
Answer 354647 by stanbon(57412) on 2011-12-06 15:45:12 (Show Source):
You can put this solution on YOUR website!Solve i^-4003
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Note i^-1 = 1/i = i^3
Keep in mind that i^4 = 1
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Your problem:
i^(-4003) = (i^3)^(4003) = i^(12009= i^9 = i^1 = i
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Cheers,
Stan
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Probability-and-statistics/542551: Bottles of a popular cola are supposed to contain 300ml of cola. There is some variation from to bottle to bottle because the filling machinery is not perfectly precise. The distribution of the contents is normal with standard deviation of Q=3 ml. An inspector who suspects that the bottler is underfilling measures the contents of six bottles. The results are
299.4 297.7 301.0
298.9 300.2 297.0
Is this convincing evidence that the mean contents of cola bottles is less than the advertised 300 ml? perform a significance test at the Q= .05level.
Z=(300-299.03)/3/6= .79 Please help
1 solutions
Answer 354644 by stanbon(57412) on 2011-12-06 15:34:04 (Show Source):
You can put this solution on YOUR website!Bottles of a popular cola are supposed to contain 300ml of cola. There is some variation from to bottle to bottle because the filling machinery is not perfectly precise. The distribution of the contents is normal with standard deviation of Q=3 ml. An inspector who suspects that the bottler is underfilling measures the contents of six bottles. The results are
299.4 297.7 301.0
298.9 300.2 297.0
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sample mean = x-bar = 299.03
Is this convincing evidence that the mean contents of cola bottles is less than the advertised 300 ml? perform a significance test at the Q= .05level.
Ho: u >= 300
Ha: u < 300 (claim)
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test statistic: t(299.03) = (299.03-300)/[1.5/sqrt(6)] = -1.5840
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p-value = P(t < -1.5840 when df = 5) = 0.0870
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Conclusion:
Since the p-value is greater than 5% fail to reject Ho.
The test results do not support the claim.
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Cheers,
Stan H.
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Probability-and-statistics/542585: what are the odds against drawing a spade greater than 3 and less than 9
1 solutions
Answer 354642 by stanbon(57412) on 2011-12-06 15:21:03 (Show Source):
You can put this solution on YOUR website! what are the odds against drawing a spade greater than 3 and less than 9
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there are 13 spades
5 of the 13 meet the criteria
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P(card meets criteria) = 5/52
P(card does not) = 47/52
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odds against = [P(card does not)/P(card does) = 47/5 = 47:5
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cheers,
Stan H.
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Probability-and-statistics/542613: The times for completing one circuit of a bicycle course are normally distributed with a mean of 80.3 minutes and a standard deviation of 7.8 minutes. An association wants to sponsor a race and provide prizes for the top 15% of riders. Where should they expect to set the cutoff time to earn a prize?
1 solutions
Answer 354641 by stanbon(57412) on 2011-12-06 15:16:37 (Show Source):
You can put this solution on YOUR website!The times for completing one circuit of a bicycle course are normally distributed with a mean of 80.3 minutes and a standard deviation of 7.8 minutes. An association wants to sponsor a race and provide prizes for the top 15% of riders. Where should they expect to set the cutoff time to earn a prize?
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Find z-value with a left tail of 0.85
invNorm(0.85) = 1.0364
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Find the correspondiing raw score value using x = zs+u
x = 1.0364*7.8+80.3
x = 88.38 munutes
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Cheers,
Stan H.
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Probability-and-statistics/542634: Carl decides to answer the following questions about the population of vegetables from these sample statistics:
Carl calculates the z-score corresponding to the weight 196 oz.
Using the table (column .00), Carl sees the area associated with this z-score is 0.
Carl rounds this value to the nearest thousandth or 0.
Now, Carl subtracts 0.50 - 0. = %.
1 solutions
Answer 354639 by stanbon(57412) on 2011-12-06 15:12:47 (Show Source):
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